Problem

Source: Albanian Mathematical Olympiad 12 GRADE 2011--Question 2

Tags: Euler, modular arithmetic, number theory unsolved, number theory



Find all the values that can take the last digit of a "perfect" even number. (The natural number $n$ is called "perfect" if the sum of all its natural divisors is equal twice the number itself.For example: the number $6$ is perfect ,because $1+2+3+6=2\cdot6$).